ON ALMOST PARACONTACT ALMOST PARACOMPLEX RIEMANNIAN MANIFOLDS

Almost paracontact manifolds of odd dimension having an almost paracomplex structure on the paracontact distribution are studied. The components of the fundamental (0,3)-tensor, derived by the covariant derivative of the structure endo-morphism and the metric on the considered manifolds in each of the basic classes are obtained. Then, the case of the lowest dimension 3 of these manifolds is considered. An associated tensor of the Nijenhuis tensor is introduced and the studied manifolds are characterized with respect to this pair of tensors. Moreover, a cases of paracontact and para-Sasakian types are commented. A family of examples is given.